But Lynch’s campaign immediately rejected the offer, saying there should be at least four wide-ranging debates. In addition, Lynch’s camp complained that some of the advocacy groups Markey wants to host the issue-specific debates have been supportive of Markey’s bid for Senate.

The back-and-forth between the two Democratic rivals is part of an early tussle over the debate schedule as both men jockey for advantage in the public eye. Elizabeth Warren and Scott Brown had a similar scuffles while trying to negotiate their own schedule ahead of last year’s Senate race.

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Markey, who initially said he did not want to negotiate the debate schedule through the news media, blasted out his proposed debate plan in a press release on Friday.

His schedule calls for one wide-ranging debate each in Springfield and Boston, sponsored by independent news organizations, and four issue-focused debates sponsored by news organizations and advocacy groups, to be held around the state. The topics, he said, could include education, jobs and the economy, public safety and national security, and “equal opportunity.”

“The voters deserve to hear the Senate candidates debate the issues that matter most to Massachusetts,” Markey’s campaign manager, Sarah Benzing, said in a statement. “With such a short primary, this proposed plan is aggressive and will bring the debate forum to as many voters as possible throughout the state.”

Lynch’s spokesman, Conor Yunits, quickly rejected the proposal, saying it was “not enough.” He said there should be at least four wide-ranging debates and the issue debates should not be sponsored by advocacy groups.

Markey has suggested, for example, that the “equal opportunity” debate be sponsored by abortion rights groups that have been highly critical of Lynch’s history of opposition to legalized abortion. In addition, Markey’s camp has suggested that public safety debate be sponsored by Stop Handgun Violence, a group that recently held a rally with Markey.

Yunits said the issue-focused debates should be sponsored by neutral groups such as the news media or universities.

“As I have said many times over the past few weeks, I believe we should hold as many debates as this short election time frame allows, including general issue debates in all parts of the state from Pittsfield, and New Bedford to Lowell and Worcester,” Lynch said in a statement. “I know there is strong demand across the state for debates, and we have had at least 15 organizations or media outlets express interest.”